The $80 \%$ confidence interval for the proportion of students who drink coffee daily is $(0.20,0.46)$. What point estimate was used to construct the confidence interval? Round to 3 decimal places.

Step 1 ：The $80 \%$ confidence interval for the proportion of students who drink coffee daily is $(0.20,0.46)$. We are asked to find the point estimate used to construct this confidence interval.

Step 2 ：The point estimate used to construct a confidence interval is the midpoint of the interval. This is because the point estimate is the best guess at the population parameter, and the confidence interval is constructed around this point estimate.

Step 3 ：Therefore, to find the point estimate, we need to calculate the midpoint of the interval $(0.20,0.46)$.

Step 4 ：Let's denote the lower bound of the interval as \(a\) and the upper bound as \(b\). In our case, \(a = 0.2\) and \(b = 0.46\).

Step 5 ：The formula to calculate the midpoint is \(\frac{a + b}{2}\). Substituting the given values, we get \(\frac{0.2 + 0.46}{2} = 0.33\).

Step 6 ：Final Answer: The point estimate used to construct the confidence interval is \(\boxed{0.33}\).